Remarks on a Fuzzy Approach to Flexible Database Querying, Its Extension and Relation to Data Mining and Summarization - Advanced Database Query Systems - page 128

Computation of a Matching Degree

Flexible fuzzy queries contain ambiguously and imprecisely specified conditions and thus they are as-
sumed to match data to a degree . The matching degree is computed for particular linguistic terms as
shown in Table 1. We omit some details in Table 1 - for a comprehensive discussion see, e.g., (Kacprzyk
& Zadrożny, 2001b).
The partial matching degrees calculated for atomic conditions (subconditions) are aggregated in
linguistic quantifier guided way, in accordance with Zadehs' approach (Zadeh, 1983), i.e., using the
following formula:

n

∑

md

i

md = m

i = 1

(19)

Q

n

where md stands for the overall matching degree and md i 's denote partial matching degrees computed
for n component conditions.

BIPOLAR QUERIES AS A NEXT STEP IN FUZZY QUERYING

In the previous sections we have presented the use of fuzzy logic in database querying in a rather tra-
ditional setting by essentially extending the standard SQL querying language in a straightforward way.
Now, we will briefly outline some new direction in flexible querying which makes possible to even
better represent complex user's preferences.
Another aspect of dealing with user preferences which is becoming more and more a topic of inten-
sive research is related to so called bipolar queries that are basically meant as involving both positive
and negative evaluation of data sought. The name “bipolar queries” was introduced by Dubois & Prade
(2002). However, the roots of this concept should be traced back to a much earlier work of Lacroix &

Table 1. Matching degree calculation of a tuple t and atomic conditions containing various linguistic
terms where: AT 1 , AT 2 , AT denote attributes; AT[t] denotes the value of attribute AT at a tuple t; FV
and μ FV denote numeric fuzzy values and their membership function; μ FV ; MOD and η denote modifiers
and their associated functions; FR, μ FR denote fuzzy relations and their membership functions; FS, μ FS
denote fuzzy set constants and their membership functions.

Linguistic term type Atomic condition form Formula for the calculation

of matching degree

Numeric fuzzy value AT = FV μ F V( A T[ t ] )

Numeric fuzzy value
with a modifier

AT = MOD FV η ( μ F V( A T[ t ] ))

Fuzzy relation AT 1 FR AT 2 μ F R( A T1 [ t ] −A T2 [ t ] )

Fuzzy set constant AT in FS μ F S( A T[ t ] )